Sid Miller, EQC chief executive, has seen the extent of the damage first hand. He went to Christchurch resident Cate Jones' house in response to Newshub's investigation, and saw the cracks for himself.

Ms Jones is just one example of a very big problem - one of hundreds of Christchurch people who brought a home only to later find out the damage hadn't been repaired properly.

Mr Miller admitted that if EQC accepts liability, the problem is about to cost the taxpayer hundreds of millions of dollars.

"Yes, we have a problem in that space," he told Newshub.

"Is it $100m? $200m? $300m? I don't know."

Photo credit: Newshub.

When asked if he could rule out it costing a billion dollars, Mr Miller replied: "None of us can rule that out."

The unlucky homeowners who find themselves in this situation are called 'on solds'. Here's how the problem comes about:

A house has its earthquake damage assessed and repaired by EQC. It is then "on sold".

The new owners find undetected damage and faulty repairs, but they are stuck because they can't claim insurance - and they can only get a maximum of $115,000 out of EQC.

The new owner is often left with damage often costing hundreds of thousands.

And nobody will pay.

It means families like Ms Jones' are trapped with no way out.

She says she is massively out of pocket, and the house is their "biggest investment".

EQC repaired and cleared the house over six years ago. It has been sold twice since then, with Ms Jones' family buying it in good faith.

"There's cracks everywhere," she said.

"It is EQC's stuff-up."

The repair bill is huge - between $200,000 and $400,000 for her house alone.

The sad reality is the family's mortgage is now bigger than the value of their home, meaning they are financially wrecked because of what happened.

Mr Miller is sympathetic.

"It's a horrible story," he told Ms Jones.

"I can't say anything more than that in terms of the position you are in. I'm sorry."

He also made a public apology to all of those affected.

"I absolutely accept that these people are in very difficult positions. I apologise that they are in these positions."

The Government has backed EQC's public apology, with Minister Megan Woods saying she "absolutely" supported it.

"I am pleased EQC has given that apology."

Up until now the extent of this problem was unknown. However Newshub can now reveal there are 664 registered cases just like Ms Jones', as well as an unknown number of unregistered ones.

Photo credit: Newshub.

The problem is certain to be much more widespread than the official figure because of people like Donna O'Malley, who are not registered with EQC yet. Her house also worth less than the mortgage.

She said the house was sold to her in good faith and EQC need to put it right.

Taking responsibility will be expensive, because some of the on-sold houses will cost up to a million dollars to repair.

Ms Woods is aware a big bill is coming if it takes liability.

"We are talking hundreds of millions," she said.

Asked if it could cost a billion dollars, she replied: "It could."

She said she had ordered Treasury forecast exactly how much the bill could be.

"I don't want to wake up one morning and find a billion-dollar bill on my desk that I have to go and tell the Minister of Finance about.

"I want to know what is coming and for us to have a plan in place to deal with it."

The next steps are for a 'test case' where a court decides whether EQC has liability or not, but the public apology and preparation for a potential billion-dollar bill show the Government is well on the way to doing that.